VSP Meshing. Rob McDonald Cal Poly. VSP Workshop
|
|
- Brianne Chambers
- 6 years ago
- Views:
Transcription
1 VSP Meshing Rob McDonald Cal Poly VSP Workshop
2 Paths to Cart3D Quadrilateral Wireframe Export CART3d File (.tri) Unintersected Triangle Wireframe CompGeom Export CART3d File (.tri) CFD Mesh Output.tri Smooth Bezier Surface Cart3D intersect Intersected Triangle Wireframe Triangle Mesh 2
3 Paths to Cart3D Quadrilateral Wireframe Export CART3d File (.tri) Unintersected Triangle Wireframe CompGeom Export CART3d File (.tri) CFD Mesh Output.tri Smooth Bezier Surface Cart3D intersect Intersected Triangle Wireframe Triangle Mesh 3
4 Unintersected Triangle Wireframe Intersected Triangle Wireframe Quadrilateral Wireframe Triangle Mesh 4
5 Pros / Cons of Paths Unintersected CompGeom CFD Mesh Pros Speed Robustness Derivatives with design framework Pros Speed Robustness Special cases Subsurfaces Pros Triangle Quality Special cases Subsurfaces Negative Volume Actuator Disk Cons Robustness Coincident faces Nacelles Extra step Cons Robustness Recommended for Cart3D Today Cons Robustness 5
6 Export Unintersected (before)
7 Export Unintersected (after) 7
8 8
9 Execute CompGeom (before)
10 Execute CompGeom (after) 1 10
11 Export CompGeom
12 Practice Session Unintersected CompGeom Save for Cart3D tutorial Resolution Effects (quads to triangles directly) Num Pts Num XSecs 12
13 CFD Mesh Generator 13
14 CFD Mesh Surface mesh generator Isotropic triangles (no stretching) Smooth Bezier surfaces Bezier intersection curves Subsurfaces Negative volume Actuator disk Sourcing control Curvature control Optional wakes Optional half-models Optional domain modeling Preferred for most CFD tools CBAero Pointwise AFLR3 Fun3D FlightStream TetGen etc. 14
15 Local Radius of Curvature r Greatest Principal Normal Curvature r = 1 k 15
16 Curvature Meshing Criteria Max Gap Num Circle Segments g l l Num Circle Segments = 8 $ & l = % '& r > g; 2 2 r g g 2 r g; 2 g # % l = $ % & N > 2; N 2; r 2 sin( π N ) r 4 N 16
17 Growth Ratio Limiter Growth Ratio X Limits length of next edge to ratio of current edge. 17
18 Rigorous 3D Growth Limiting Off (faster) On (slower) 18
19 Source Types Point Line Box 19
20 Sourcing Attached to components (u, w) Size in model units (length) Sphere of influence (radius) 20
21 Mesh Criteria Precedence Smallest Edge Across Criteria Subject to Constraints Above & Below Sources Max Edge Len Growth Ratio Max Gap Num Circle Segments Min Edge Len 21
22 Turning Mesh Criteria OFF Sometimes it is useful to turn a mesh criteria OFF. Criteria Direction Value Scaled? Max Edge Len large (scaled) Growth Ratio large 10.0 Sources none Max Gap large 10.0 (scaled) Num Circle Segments small Min Edge Len small (scaled) Max = Min will turn OFF Max Gap & Num Circle Segments Sources Max Edge Len Growth Ratio Max Gap Num Circle Segments Min Edge Len 22
23 Meshing Strategy 1. Set Max based on model dimensions Set Min = Max (turning off MG and NCS) No Sources Adjust Max & Min until satisfied (uniform coarsest) 2. Set Min to smaller value Say Min = Max/20 3. Choose MG or NCS as preferred curvature parameter (CP) Set other curvature parameter (OCP) OFF Adjust CP until satisfied Adjust Min as required (are smallest edges small enough?) 4. Adjust OCP (optional) 5. Add mesh sources as required Resolve flow features 23
24 Top Model Constant curvature (constant radius) Increasing curvature (decreasing radius) Extreme curvature (vanishing radius) File on the wiki. 24
25 CFD Mesh GUI 25
26 Global Global & Curvature Meshing Criteria Rigorous Limiting Switch Global Source Adjustment Intersect Subsurfaces Choose Set Mesh Output Go Button 26
27 Display Display Switches Mesh Output Go Button 27
28 Output Multi-Solid STL Switch File Output Switches File Paths File Browser Button Mesh Output Go Button 28
29 Sources Component Chooser Select Surface Source Type Chooser Component Source List Add/Delete Buttons Individual Source Editor Mesh Output Go Button 29
30 Domain Half Mesh Switch Far Field Switch Far Field Mesh Size Far Field Component List Far Field Comp/Box Switch Symmetry Plane Split Far Field Box Controls Mesh Output Go Button 30
31 Domain Modeling 31
32 Symmetry Plane Splitting 32
33 Wakes Wake Length Wake Angle Component Chooser Wake Switch Mesh Output Go Button 33
34 Negative Components Gen Tab Negative Volume 34
35 Negative Pod 35
36 Propulsion Modeling 36
37 Actuator Disk 37
38 Actuator Disk in Duct 38
39 Practice Session CFD Mesh Top model Experiment with meshing parameters Turn all criteria off play with one at a time Follow meshing strategy CFD Mesh Your model Follow meshing strategy 39
40 Command Line / API vsp airplane.vsp3 -script myscript.vspscript!! # -des airplane.des # Apply design file! # vspscript # Batch only executable! // Script to export Unintersected Cart3D tri file! void main() { ExportFile( output.tri, 0, EXPORT_CART3D ); }! // Script to execute CompGeom and export Cart3D tri file! void main() { ComputeCompGeom( 0, false, NO_FILE_TYPE ); ExportFile( output.tri, 0, EXPORT_CART3D ); }! // Script to execute CFDMesh and export Cart3D tri file! void main() { ComputeCFDMesh( 0, EXPORT_CART3D ); }! 40
VSP File Types & VSP Meshing
VSP File Types & VSP Meshing Rob McDonald Cal Poly VSP Workshop August 21 & 22, 2014 VSP v2 Input Representations Input Parametric geometry (vsp) Background image (jpg) Surface textures (tga, jpg) Automation
More informationVSP File Types & VSP Meshing
VSP File Types & VSP Meshing Rob McDonald Cal Poly VSP Workshop August 23, 2012 VSP Input Representations Input Parametric geometry (vsp) Background image (jpg) Surface textures (tga, jpg) Automation script
More informationAn Advanced Extensible Parametric Geometry Engine for Multi-Fidelity and Multi-Physics Analysis in Conceptual Design
An Advanced Extensible Parametric Geometry Engine for Multi-Fidelity and Multi-Physics Analysis in Conceptual Design Rob McDonald & David Marshall Cal Poly Andy Ko. JR Gloudemans NASA Glenn July 23, 2012
More informationCAD-BASED WORKFLOWS. VSP Workshop 2017
CAD-BASED WORKFLOWS VSP Workshop 2017 RESEARCH IN FLIGHT COMPANY Established 2012 Primary functions are the development, marketing and support of FlightStream and the development of aerodynamic solutions
More informationOpenVSP Workshop (6) Rob McDonald. Cliffs Resort, Pismo Beach CA August 30 Sept 1, 2017
OpenVSP Workshop (6) Rob McDonald Cliffs Resort, Pismo Beach CA August 30 Sept 1, 2017 1 Geometry as Origin of Analysis (Design) Shape is fundamental starting point for physics-based analysis Aerodynamics
More informationIntroduction to ANSYS ICEM CFD
Lecture 4 Volume Meshing 14. 0 Release Introduction to ANSYS ICEM CFD 1 2011 ANSYS, Inc. March 21, 2012 Introduction to Volume Meshing To automatically create 3D elements to fill volumetric domain Generally
More informationVehicle Sketch Pad Applied To Propulsion-Airframe Integration
Vehicle Sketch Pad Applied To Propulsion-Airframe Integration Presented by Steven H. Berguin stevenberguin@gatech.edu 1. Introduction 2. Modeling & Simulation 3. Example: Isolated Nacelle (Powered) 4.
More information274 Curves on Surfaces, Lecture 5
274 Curves on Surfaces, Lecture 5 Dylan Thurston Notes by Qiaochu Yuan Fall 2012 5 Ideal polygons Previously we discussed three models of the hyperbolic plane: the Poincaré disk, the upper half-plane,
More informationHPC Computer Aided CINECA
HPC Computer Aided Engineering @ CINECA Raffaele Ponzini Ph.D. CINECA SuperComputing Applications and Innovation Department SCAI 16-18 June 2014 Segrate (MI), Italy Outline Open-source CAD and Meshing
More information2. MODELING A MIXING ELBOW (2-D)
MODELING A MIXING ELBOW (2-D) 2. MODELING A MIXING ELBOW (2-D) In this tutorial, you will use GAMBIT to create the geometry for a mixing elbow and then generate a mesh. The mixing elbow configuration is
More informationCATIA Surface Design
CATIA V5 Training Exercises CATIA Surface Design Version 5 Release 19 September 2008 EDU_CAT_EN_GS1_FX_V5R19 Table of Contents (1/2) Creating Wireframe Geometry: Recap Exercises 4 Creating Wireframe Geometry:
More informationContribution to GMGW 1
Contribution to GMGW 1 Rocco Nastasia, Saurabh Tendulkar, Mark Beall Simmetrix Inc., Clifton Park, NY 12065 Riccardo Balin, Scott Wurst, Ryan Skinner, Kenneth E. Jansen Department of Aerospace Engineering
More informationInaugural OpenVSP Workshop
Inaugural OpenVSP Workshop Rob McDonald San Luis Obispo August 22, 2012 Geometry as Origin of Analysis (Design) Shape is fundamental starting point for physics-based analysis Aerodynamics Structures Aeroelasticity
More informationCurve and Surface Basics
Curve and Surface Basics Implicit and parametric forms Power basis form Bezier curves Rational Bezier Curves Tensor Product Surfaces ME525x NURBS Curve and Surface Modeling Page 1 Implicit and Parametric
More informationPlanar quad meshes from relative principal curvature lines
Planar quad meshes from relative principal curvature lines Alexander Schiftner Institute of Discrete Mathematics and Geometry Vienna University of Technology 15.09.2007 Alexander Schiftner (TU Vienna)
More informationBest Practices: Volume Meshing Kynan Maley
Best Practices: Volume Meshing Kynan Maley Volume Meshing Volume meshing is the basic tool that allows the creation of the space discretization needed to solve most of the CAE equations for: CFD Stress
More informationLecture 7: Mesh Quality & Advanced Topics. Introduction to ANSYS Meshing Release ANSYS, Inc. February 12, 2015
Lecture 7: Mesh Quality & Advanced Topics 15.0 Release Introduction to ANSYS Meshing 1 2015 ANSYS, Inc. February 12, 2015 Overview In this lecture we will learn: Impact of the Mesh Quality on the Solution
More informationMATERIAL FOR A MASTERCLASS ON HYPERBOLIC GEOMETRY. Timeline. 10 minutes Exercise session: Introducing curved spaces
MATERIAL FOR A MASTERCLASS ON HYPERBOLIC GEOMETRY Timeline 10 minutes Introduction and History 10 minutes Exercise session: Introducing curved spaces 5 minutes Talk: spherical lines and polygons 15 minutes
More informationAdvanced Meshing Tools
Page 1 Advanced Meshing Tools Preface Using This Guide More Information Conventions What's New? Getting Started Entering the Advanced Meshing Tools Workbench Defining the Surface Mesh Parameters Setting
More informationUNIVERSITI TEKNOLOGI MALAYSIA SSE 1893 ENGINEERING MATHEMATICS TUTORIAL 5
UNIVERSITI TEKNOLOGI MALAYSIA SSE 189 ENGINEERING MATHEMATIS TUTORIAL 5 1. Evaluate the following surface integrals (i) (x + y) ds, : part of the surface 2x+y+z = 6 in the first octant. (ii) (iii) (iv)
More informationIndiana State Math Contest Geometry
Indiana State Math Contest 018 Geometry This test was prepared by faculty at Indiana University - Purdue University Columbus Do not open this test booklet until you have been advised to do so by the test
More informationDifferential Geometry: Circle Patterns (Part 1) [Discrete Conformal Mappinngs via Circle Patterns. Kharevych, Springborn and Schröder]
Differential Geometry: Circle Patterns (Part 1) [Discrete Conformal Mappinngs via Circle Patterns. Kharevych, Springborn and Schröder] Preliminaries Recall: Given a smooth function f:r R, the function
More informationGEOMETRY MODELING & GRID GENERATION
GEOMETRY MODELING & GRID GENERATION Dr.D.Prakash Senior Assistant Professor School of Mechanical Engineering SASTRA University, Thanjavur OBJECTIVE The objectives of this discussion are to relate experiences
More informationNew York Tutorials are designed specifically for the New York State Learning Standards to prepare your students for the Regents and state exams.
Tutorial Outline New York Tutorials are designed specifically for the New York State Learning Standards to prepare your students for the Regents and state exams. Math Tutorials offer targeted instruction,
More informationMath 265 Exam 3 Solutions
C Roettger, Fall 16 Math 265 Exam 3 Solutions Problem 1 Let D be the region inside the circle r 5 sin θ but outside the cardioid r 2 + sin θ. Find the area of D. Note that r and θ denote polar coordinates.
More informationCalypso Construction Features. Construction Features 1
Calypso 1 The Construction dropdown menu contains several useful construction features that can be used to compare two other features or perform special calculations. Construction features will show up
More information3. MODELING A THREE-PIPE INTERSECTION (3-D)
3. MODELING A THREE-PIPE INTERSECTION (3-D) This tutorial employs primitives that is, predefined GAMBIT modeling components and procedures. There are two types of GAMBIT primitives: Geometry Mesh Geometry
More informationGeometric Entities for Pilot3D. Copyright 2001 by New Wave Systems, Inc. All Rights Reserved
Geometric Entities for Pilot3D Copyright 2001 by New Wave Systems, Inc. All Rights Reserved Introduction on Geometric Entities for Pilot3D The best way to develop a good understanding of any Computer-Aided
More informationOptimizing triangular meshes to have the incrircle packing property
Packing Circles and Spheres on Surfaces Ali Mahdavi-Amiri Introduction Optimizing triangular meshes to have p g g the incrircle packing property Our Motivation PYXIS project Geometry Nature Geometry Isoperimetry
More informationGlossary of dictionary terms in the AP geometry units
Glossary of dictionary terms in the AP geometry units affine linear equation: an equation in which both sides are sums of terms that are either a number times y or a number times x or just a number [SlL2-D5]
More informationEvaluating the Quality of Triangle, Quadrilateral, and Hybrid Meshes Before and After Refinement
Rensselaer Polytechnic Institute Advanced Computer Graphics, Spring 2014 Final Project Evaluating the Quality of Triangle, Quadrilateral, and Hybrid Meshes Before and After Refinement Author: Rebecca Nordhauser
More informationQuick Surface Reconstruction
CATIA V5 Training Exercises Quick Surface Reconstruction Version 5 Release 19 August 2008 EDU_CAT_EN_QSR_FX_V5R19 1 Table of Contents Master Exercise Presentation:Plastic Bottle 3 Design Intent - Plastic
More informationCATIA V5 Parametric Surface Modeling
CATIA V5 Parametric Surface Modeling Version 5 Release 16 A- 1 Toolbars in A B A. Wireframe: Create 3D curves / lines/ points/ plane B. Surfaces: Create surfaces C. Operations: Join surfaces, Split & Trim
More informationOpenVSP Workshop. Rob McDonald. San Luis Obispo August 20, 2014
OpenVSP Workshop Rob McDonald San Luis Obispo August 20, 2014 Geometry as Origin of Analysis (Design) Shape is fundamental starting point for physics-based analysis Aerodynamics Structures Aeroelasticity
More informationGood Continuation of Boundary Contour
Thinh Nguyen 10/18/99 Lecture Notes CS294 Visual Grouping and Recognition Professor: Jitendra Malik Good Continuation of Boundary Contour Review Factors that leads to grouping. Similarity (brightness,
More information3. The three points (2, 4, 1), (1, 2, 2) and (5, 2, 2) determine a plane. Which of the following points is in that plane?
Math 4 Practice Problems for Midterm. A unit vector that is perpendicular to both V =, 3, and W = 4,, is (a) V W (b) V W (c) 5 6 V W (d) 3 6 V W (e) 7 6 V W. In three dimensions, the graph of the equation
More information12 m. 30 m. The Volume of a sphere is 36 cubic units. Find the length of the radius.
NAME DATE PER. REVIEW #18: SPHERES, COMPOSITE FIGURES, & CHANGING DIMENSIONS PART 1: SURFACE AREA & VOLUME OF SPHERES Find the measure(s) indicated. Answers to even numbered problems should be rounded
More informationLength and Area. Charles Delman. April 20, 2010
Length and Area Charles Delman April 20, 2010 What is the length? Unit Solution Unit 5 (linear) units What is the length? Unit Solution Unit 5 2 = 2 1 2 (linear) units What is the perimeter of the shaded
More informationAnswers to Geometry Unit 5 Practice
Lesson 0- Answers to Geometry Unit 5 Practice. a. Rectangle; Sample answer: It has four right angles. b. length: units; width: 9 units A 5 bh 7 units. 96 units. a. Parallelogram; Sample answer: Opposite
More informationCS354 Computer Graphics Surface Representation IV. Qixing Huang March 7th 2018
CS354 Computer Graphics Surface Representation IV Qixing Huang March 7th 2018 Today s Topic Subdivision surfaces Implicit surface representation Subdivision Surfaces Building complex models We can extend
More informationShippensburg Math & Computer Day 2013 Individual Math Contest
Shippensburg Math & Computer Day 2013 Individual Math Contest 1. Row n of Pascal s Triangle lists all the coefficients of the expansion of (1 + x) n. What is the smallest value of n for which the sum of
More informationV = 2πx(1 x) dx. x 2 dx. 3 x3 0
Wednesday, September 3, 215 Page 462 Problem 1 Problem. Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the region (y = x, y =, x = 2)
More information15. SAILBOAT GEOMETRY
SAILBOAT GEOMETRY 15. SAILBOAT GEOMETRY In this tutorial you will import a STEP file that describes the geometry of a sailboat hull. You will split the hull along the symmetry plane, create a flow volume
More informationMAC2313 Final A. a. The vector r u r v lies in the tangent plane of S at a given point. b. S f(x, y, z) ds = R f(r(u, v)) r u r v du dv.
MAC2313 Final A (5 pts) 1. Let f(x, y, z) be a function continuous in R 3 and let S be a surface parameterized by r(u, v) with the domain of the parameterization given by R; how many of the following are
More informationRay Tracing I. History
History Ray Tracing came from the Physics of lens making. The process was that of drawing lines or rays through a glass shape to determine it s lens properties. It is also related to early perspective
More informationLesson 3: Surface Creation
Lesson 3: Surface Creation In this lesson, you will learn how to create surfaces from wireframes. Lesson Contents: Case Study: Surface Creation Design Intent Stages in the Process Choice of Surface Sweeping
More informationf xx (x, y) = 6 + 6x f xy (x, y) = 0 f yy (x, y) = y In general, the quantity that we re interested in is
1. Let f(x, y) = 5 + 3x 2 + 3y 2 + 2y 3 + x 3. (a) Final all critical points of f. (b) Use the second derivatives test to classify the critical points you found in (a) as a local maximum, local minimum,
More informationRHINOCEROS AND NURBS MODELING
Introduction RHINOCEROS AND NURBS MODELING There are three main ways to create a 3D computer model using 3D applications. Each has particular advantages and drawbacks, and the ability to create (or convert
More informationCS 523: Computer Graphics, Spring Differential Geometry of Surfaces
CS 523: Computer Graphics, Spring 2009 Shape Modeling Differential Geometry of Surfaces Andrew Nealen, Rutgers, 2009 3/4/2009 Recap Differential Geometry of Curves Andrew Nealen, Rutgers, 2009 3/4/2009
More informationViscous Hybrid Mesh Generation
Tutorial 4. Viscous Hybrid Mesh Generation Introduction In cases where you want to resolve the boundary layer, it is often more efficient to use prismatic cells in the boundary layer rather than tetrahedral
More informationThe Law of Reflection
If the surface off which the light is reflected is smooth, then the light undergoes specular reflection (parallel rays will all be reflected in the same directions). If, on the other hand, the surface
More informationdq dt I = Irradiance or Light Intensity is Flux Φ per area A (W/m 2 ) Φ =
Radiometry (From Intro to Optics, Pedrotti -4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Total energy radiating from the body over some time is Q total Radiant
More informationPURPLE COMET MATH MEET April 2011 HIGH SCHOOL - PROBLEMS. The ratio of 3 to the positive number n is the same as the ratio of n to 192. Find n.
PURPLE COMET MATH MEET April 2011 HIGH SCHOOL - PROBLEMS Copyright Titu Andreescu and Jonathan Kane Problem 1 The ratio of 3 to the positive number n is the same as the ratio of n to 192. Find n. Problem
More informationSurface Mesh Generation
Surface Mesh Generation J.-F. Remacle Université catholique de Louvain September 22, 2011 0 3D Model For the description of the mesh generation process, let us consider the CAD model of a propeller presented
More informationPlot four points A, B, C and D on the grid to make a rectangle ABCD of length 6 cm and width 4 cm. (2)
Q1. (a) Here is a centimetre grid. Plot four points A, B, C and D on the grid to make a rectangle ABCD of length 6 cm and width 4 cm. (2) (b) Tick whether each statement is always true, sometimes true
More informationMATH 104 First Midterm Exam - Fall (d) A solid has as its base the region in the xy-plane the region between the curve y = 1 x2
MATH 14 First Midterm Exam - Fall 214 1. Find the area between the graphs of y = x 2 + x + 5 and y = 2x 2 x. 1. Find the area between the graphs of y = x 2 + 4x + 6 and y = 2x 2 x. 1. Find the area between
More informationGeometric Modeling Systems
Geometric Modeling Systems Wireframe Modeling use lines/curves and points for 2D or 3D largely replaced by surface and solid models Surface Modeling wireframe information plus surface definitions supports
More informationLagrange multipliers October 2013
Lagrange multipliers 14.8 14 October 2013 Example: Optimization with constraint. Example: Find the extreme values of f (x, y) = x + 2y on the ellipse 3x 2 + 4y 2 = 3. 3/2 1 1 3/2 Example: Optimization
More information2017-ACTM Regional Mathematics Contest
2017-TM Regional Mathematics ontest Geometry nswer each of the multiple-choice questions and mark your answers on that answer sheet provided. When finished with the multiple-choice items, then answer the
More informationLecture 6: CAD Import Release. Introduction to ANSYS Fluent Meshing
Lecture 6: CAD Import 14.5 Release Introduction to ANSYS Fluent Meshing 1 Fluent Meshing 14.5 Assembly meshing Workflow This Lecture Tessellated or Conformal CAD import Cap Inlet/Outlets, Create Domains/BOI
More informationGeometry Vocabulary. acute angle-an angle measuring less than 90 degrees
Geometry Vocabulary acute angle-an angle measuring less than 90 degrees angle-the turn or bend between two intersecting lines, line segments, rays, or planes angle bisector-an angle bisector is a ray that
More informationIntroduction to CFX. Workshop 2. Transonic Flow Over a NACA 0012 Airfoil. WS2-1. ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.
Workshop 2 Transonic Flow Over a NACA 0012 Airfoil. Introduction to CFX WS2-1 Goals The purpose of this tutorial is to introduce the user to modelling flow in high speed external aerodynamic applications.
More informationChapter 5.4: Sinusoids
Chapter 5.4: Sinusoids If we take our circular functions and unwrap them, we can begin to look at the graphs of each trig function s ratios as a function of the angle in radians. We will begin by looking
More informationOffset Triangular Mesh Using the Multiple Normal Vectors of a Vertex
285 Offset Triangular Mesh Using the Multiple Normal Vectors of a Vertex Su-Jin Kim 1, Dong-Yoon Lee 2 and Min-Yang Yang 3 1 Korea Advanced Institute of Science and Technology, sujinkim@kaist.ac.kr 2 Korea
More informationWorkshop 3: Cutcell Mesh Generation. Introduction to ANSYS Fluent Meshing Release. Release ANSYS, Inc.
Workshop 3: Cutcell Mesh Generation 14.5 Release Introduction to ANSYS Fluent Meshing 1 2011 ANSYS, Inc. December 21, 2012 I Introduction Workshop Description: CutCell meshing is a general purpose meshing
More informationAnsoft HFSS Mesh Menu
Ansoft HFSS After you have seeded your object, you must create the finite element mesh from which the variables and values of your model will be computed. The Mesh menu allows you to: Create or delete
More informationChapter 23. Geometrical Optics (lecture 1: mirrors) Dr. Armen Kocharian
Chapter 23 Geometrical Optics (lecture 1: mirrors) Dr. Armen Kocharian Reflection and Refraction at a Plane Surface The light radiate from a point object in all directions The light reflected from a plane
More informationFreeStyle Shaper & Optimizer
FreeStyle Shaper & Optimizer Preface What's New Getting Started Basic Tasks Advanced Tasks Workbench Description Customizing Glossary Index Dassault Systèmes 1994-99. All rights reserved. Preface CATIA
More information3D Modeling: Surfaces
CS 430/536 Computer Graphics I 3D Modeling: Surfaces Week 8, Lecture 16 David Breen, William Regli and Maxim Peysakhov Geometric and Intelligent Computing Laboratory Department of Computer Science Drexel
More informationacute angle An angle with a measure less than that of a right angle. Houghton Mifflin Co. 2 Grade 5 Unit 6
acute angle An angle with a measure less than that of a right angle. Houghton Mifflin Co. 2 Grade 5 Unit 6 angle An angle is formed by two rays with a common end point. Houghton Mifflin Co. 3 Grade 5 Unit
More information1. POINTS, LINES, AND ANGLES
Tutorial Outline California Tutorials are designed specifically for the California Common Core State Standards and the California Next Generation Science Standards to prepare students for the Smarter Balanced
More informationLagrange multipliers 14.8
Lagrange multipliers 14.8 14 October 2013 Example: Optimization with constraint. Example: Find the extreme values of f (x, y) = x + 2y on the ellipse 3x 2 + 4y 2 = 3. 3/2 Maximum? 1 1 Minimum? 3/2 Idea:
More information10.1 Overview. Section 10.1: Overview. Section 10.2: Procedure for Generating Prisms. Section 10.3: Prism Meshing Options
Chapter 10. Generating Prisms This chapter describes the automatic and manual procedure for creating prisms in TGrid. It also discusses the solution to some common problems that you may face while creating
More informationFrom curves to surfaces. Parametric surfaces and solid modeling. Extrusions. Surfaces of revolution. So far have discussed spline curves in 2D
From curves to surfaces Parametric surfaces and solid modeling CS 465 Lecture 12 2007 Doug James & Steve Marschner 1 So far have discussed spline curves in 2D it turns out that this already provides of
More informationLesson 2: Wireframe Creation
Lesson 2: Wireframe Creation In this lesson you will learn how to create wireframes. Lesson Contents: Case Study: Wireframe Creation Design Intent Stages in the Process Reference Geometry Creation 3D Curve
More informationUser Guide. for. JewelCAD Professional Version 2.0
User Guide Page 1 of 121 User Guide for JewelCAD Professional Version 2.0-1 - User Guide Page 2 of 121 Table of Content 1. Introduction... 7 1.1. Purpose of this document... 7 2. Launch JewelCAD Professional
More informationTUTORIAL 7: Stress Concentrations and Elastic-Plastic (Yielding) Material Behavior Initial Project Space Setup Static Structural ANSYS ZX Plane
TUTORIAL 7: Stress Concentrations and Elastic-Plastic (Yielding) Material Behavior In this tutorial you will learn how to recognize and deal with a common modeling issues involving stress concentrations
More informationCurvature Berkeley Math Circle January 08, 2013
Curvature Berkeley Math Circle January 08, 2013 Linda Green linda@marinmathcircle.org Parts of this handout are taken from Geometry and the Imagination by John Conway, Peter Doyle, Jane Gilman, and Bill
More informationANSYS Workbench Guide
ANSYS Workbench Guide Introduction This document serves as a step-by-step guide for conducting a Finite Element Analysis (FEA) using ANSYS Workbench. It will cover the use of the simulation package through
More informationGEOMETRY (COMMON CORE) FACTS YOU MUST KNOW COLD FOR THE REGENTS EXAM
GEOMETRY (COMMON CORE) FACTS YOU MUST KNOW COLD FOR THE REGENTS EXAM NYS Mathematics Regents Preparation Created by: Trevor Clark Geometry [Common Core] Regents Exam Study Guide Facts You Must Know Cold
More informationOhio Tutorials are designed specifically for the Ohio Learning Standards to prepare students for the Ohio State Tests and end-ofcourse
Tutorial Outline Ohio Tutorials are designed specifically for the Ohio Learning Standards to prepare students for the Ohio State Tests and end-ofcourse exams. Math Tutorials offer targeted instruction,
More informationPrime Time (Factors and Multiples)
CONFIDENCE LEVEL: Prime Time Knowledge Map for 6 th Grade Math Prime Time (Factors and Multiples). A factor is a whole numbers that is multiplied by another whole number to get a product. (Ex: x 5 = ;
More informationElementary Planar Geometry
Elementary Planar Geometry What is a geometric solid? It is the part of space occupied by a physical object. A geometric solid is separated from the surrounding space by a surface. A part of the surface
More informationL9.5 Welcome Back! 1
L9.5 Welcome Back! 1 2 3 A blast from the past... L9.5 Label the following parts: Center Radius Apothem Center angle Side 4 A blast from the past... L9.5 Label the following parts: Center Radius Apothem
More informationUnit 13: Periodic Functions and Trig
Date Period Unit 13: Periodic Functions and Trig Day Topic 0 Special Right Triangles and Periodic Function 1 Special Right Triangles Standard Position Coterminal Angles 2 Unit Circle Cosine & Sine (x,
More informationStudy Guide and Review
State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. Euclidean geometry deals with a system of points, great circles (lines), and spheres (planes). false,
More informationMath 21a Final Exam Solutions Spring, 2009
Math a Final Eam olutions pring, 9 (5 points) Indicate whether the following statements are True or False b circling the appropriate letter No justifications are required T F The (vector) projection of
More informationAdvances in Pre-Processing
Advances in Pre-Processing Laz Foley Confidence by Design Chicago June 14, 2012 1 Outline ANSYS DesignModeler Modeling Improvements ANSYS SpaceClaim Direct Modeler Workbench Integration and Model Preparation
More information2011 James S. Rickards Fall Invitational Geometry Team Round QUESTION 1
QUESTION 1 In the diagram above, 1 and 5 are supplementary and 2 = 6. If 1 = 34 and 2 = 55, find 3 + 4 + 5 + 6. QUESTION 2 A = The sum of the degrees of the interior angles of a regular pentagon B = The
More informationChapter 9 3D Modeling
Chapter 9 3D Modeling Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 3D Modeling Snapshot Since Mid 1980 s become common place in industry Software Types Wireframe
More informationGeometry--Unit 10 Study Guide
Class: Date: Geometry--Unit 10 Study Guide Determine whether each statement is true or false. If false, give a counterexample. 1. Two different great circles will intersect in exactly one point. A) True
More informationMath 3C Section 9.1 & 9.2
Math 3C Section 9.1 & 9.2 Yucheng Tu 11/14/2018 1 Unit Circle The unit circle comes to the stage when we enter the field of trigonometry, i.e. the study of relations among the sides and angles of an arbitrary
More informationTUTORIAL 3DESIGN. Gravotech SAS-Type3
TUTORIAL 3DESIGN Gravotech SAS-Type3 Satellite Ring Creation time: 45 minutes Level: Beginner This exercise will be done with the following material: Precious metal, Gold 18k White gold 2 A.RING SHANK
More informationLectures in Discrete Differential Geometry 3 Discrete Surfaces
Lectures in Discrete Differential Geometry 3 Discrete Surfaces Etienne Vouga March 19, 2014 1 Triangle Meshes We will now study discrete surfaces and build up a parallel theory of curvature that mimics
More informationUnit 1: Tools of Geometry
Unit 1: Tools of Geometry Geometry CP Pacing Guide First Nine Weeks Tennessee State Math Standards Know precise definitions of angle, circle, perpendicular line, parallel G.CO.A.1 line, and line segment,
More informationTutorial - Steering Wheel
Tutorial - Steering Wheel (written by Jacob Tremmel, Student at Altair) This tutorial is about modeling (CAD) and rendering of a Steering Wheel with Altair s solidthinking Evolve 9.0. 1 Modeling 1. At
More informationVoronoi Diagram. Xiao-Ming Fu
Voronoi Diagram Xiao-Ming Fu Outlines Introduction Post Office Problem Voronoi Diagram Duality: Delaunay triangulation Centroidal Voronoi tessellations (CVT) Definition Applications Algorithms Outlines
More informationChapter 23. Geometrical Optics: Mirrors and Lenses and other Instruments
Chapter 23 Geometrical Optics: Mirrors and Lenses and other Instruments HITT1 A small underwater pool light is 1 m below the surface of a swimming pool. What is the radius of the circle of light on the
More informationThis tutorial will take you all the steps required to import files into ABAQUS from SolidWorks
ENGN 1750: Advanced Mechanics of Solids ABAQUS CAD INTERFACE TUTORIAL School of Engineering Brown University This tutorial will take you all the steps required to import files into ABAQUS from SolidWorks
More informationGeometrization and the Poincaré conjecture
Geometrization and the Poincaré conjecture Jan Metzger BRIGFOS, 2008 History of the Poincaré conjecture In 1904 Poincaré formulated his conjecture. It is a statement about three dimensional geometric objects,
More information